There are known digital accelerometers using resonant force transducers for acceleration sensing. An example of the kind of force transducer used in these applications is the double resonant beam force transducer shaped as a double-ended tuning fork as disclosed in U.S. Pat. No. 4,372,173 Eer Nisse et al (1983) and International Application Publication No. WO 84/03998. These patents identify the problem of energy coupling from the beam to the force transmitting structure, known as longitudinal pumping. This is described as undesireable for its degrading of both the Q and the linearity of the transducer.
The operation of these devices is based on measurement of deviation in frequency from that established in a bias condition where no-load is applied to the transducer. The frequency measurement provided in the bias condition is used as a reference for these deviation measurements.
A technique for reducing longitudinal pumping is proposed in the above mentioned International Application by provision of the beams with a non-uniform width, so that in one configuration the beams are bowed inwardly, in an attempt to have substantially equal deflection of the beam inwardly and outwardly. The shaping required to achieve this result is stated in approximate terms as a percentage of the beam width relative to the width of the gap between the beams at the midpoint and ends of their lengths. However, the particular shaping is not determined precisely. Even with the shaping suggested the problem of longitudinal pumping is not eliminated.
The problem of energy coupling to the support structure is also the subject of U.S. Pat. No. 4,321,500 to Paros. Here, a solution is suggested in which longitudinal isolation elements from part of the transducer structure but again, the shaping is complex and the problem of longitudinal pumping is not eliminated.
The problem of energy coupling is also discussed in connection with the resonant force transducer shape proposed by British Pat. No. 2,141,231 to Kirman et al. Here, the structure of the transducer is a double-ended design with at least three coplanar beams generally parallel with one another which are supported at each end by a common mounting. No disclosure is made of a definite increase in efficiency resulting from this arrangement.
Another approach to acceleration sensing using force transducers is based on a push-pull configuration as disclosed by U.S. Pat. Nos. 4,221,131 to Albert (1980) and 4,517,841 to Peters et al (1985). The push-pull configurations generally require the use of two individual transducer elements arranged back-to-back so that the motion of their respective proof masses is in opposite directions, and this makes for a complicated design.
In all of the above cases, the magnitude of the energy loss due to longitudinal pumping in a double-ended tuning fork or single beam is related to the kinetic energy imparted to the mounting pads or proof mass. In acceleration sensors, for a given amplitude of vibration and geometry of the beam, this can be shown to be proportional to the square of the longitudinal velocity of beam supporting the proof mass. This is analogous to the displacement of the mounting pads of a resonant force transducer. It would therefore be desirable to reduce the kinetic energy imparted respectively to the mounting pads or the proof mass and so improve the performance of the force transducer in respective force and acceleration sensing applications.